Around here mechanics have only two tools in their tool boxes, duct tape and WD40. Duct tape for fixing things that move that aren't supposed to move, and WD40 for fixing things that are supposed to move, but don't. And this sounds like a job for duct tape.

Since it's old I wouldn't take a chance on cracking it by drilling through the base. I would use it as is and just try to locate it where one side can be disguised so the cord won't be so noticeable, like near a building or some plantings. You can also run the cord over the edge of the basin and down one side and tape it to the base so it's not waving around in the wind. You could disguise it further by painting the whole kit'n'kaboodle with some concrete paint, including the cord and any tape you use, so it looks like it's supposed to be there.

Seamommy, You are the Best!!! Duct tape rules!!! I wish you could see the smile on my face. I have been so discouraged that the whole thing is laying in sections on my compost pile. I wanted the fountain for the center piece of my rose garden so there is no wall or planting that would work to hide the cord coming off the fountain. But some duct tape and some creative concrete painting and I am good to go. Thank You!!!

Does your fountain have a drain hole and a rubber plug in the drain hole? They actually make a split rubber drain plug that a submersible pump cord goes through and seals tight so the water doesn't leak out. In my case, I found the manufacturer and was able to get a replacement drain plug from them.

Dwyman,
Yes! The whole thing is still on the compost pile and I decided to look at it again today. I am going to see if I can get a split rubber drain plug. Thank you very much for the suggestion!